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Mat. Zametki, 1977, Volume 22, Issue 2, Pages 231–244 (Mi mz8044)  

This article is cited in 13 scientific papers (total in 13 papers)

Uniform regularization of the problem of calculating the values of an operator

V. V. Arestov

Institute of Mathematics and Mechanics, Ural Scientific Center of the AS of USSR

Abstract: Let $X$ and $Y$ be linear normed spaces, $W$ a set in $X$, $A$ an operator from $W$ into $Y$, and $\mathfrak M$ the set $\mathfrak G$ of all operators or the set $\mathscr L$ of linear operators from $X$ into $Y$. With $\delta\ge0$ we put
$$ \nu(\delta,\mathfrak M)=\inf_{T\in\mathfrak M}\sup_{x\in W}\sup_{\|\eta-x\|_X\le\delta}\|Ax-T\eta\|_Y. $$
We discuss the connection of $\nu(\delta,\mathfrak M)$ with the Stechkin problem on best approximation of the operator $A$ in $W$ by linear bounded operators. Estimates are obtained for $\nu(\delta,\mathfrak M)$ e.g., we write the inequality, where $H(Y)$ is Jung's constant of the space $Y$, and $\Omega(t)$ is the modulus of continuity of $A$ in $W$.

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English version:
Mathematical Notes, 1977, 22:2, 618–626

Bibliographic databases:

UDC: 517.5
Received: 24.03.1977

Citation: V. V. Arestov, “Uniform regularization of the problem of calculating the values of an operator”, Mat. Zametki, 22:2 (1977), 231–244; Math. Notes, 22:2 (1977), 618–626

Citation in format AMSBIB
\by V.~V.~Arestov
\paper Uniform regularization of the problem of calculating the values of an operator
\jour Mat. Zametki
\yr 1977
\vol 22
\issue 2
\pages 231--244
\jour Math. Notes
\yr 1977
\vol 22
\issue 2
\pages 618--626

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    This publication is cited in the following articles:
    1. V. V. Arestov, “Approximation of unbounded operators by bounded operators and related extremal problems”, Russian Math. Surveys, 51:6 (1996), 1093–1126  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. O. A. Timoshin, “The best approximation to the operator of the second mixed derivative”, Izv. Math., 62:1 (1998), 191–200  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. G. V. Khromova, “On the moduli of continuity of unbounded operators”, Russian Math. (Iz. VUZ), 50:9 (2006), 67–74  mathnet  mathscinet
    4. Babenko Yu., Skorokhodov D., “Stechkin's Problem for Differential Operators and Functionals of First and Second Orders”, J. Approx. Theory, 167 (2013), 173–200  crossref  isi
    5. V. I. Maksimov, “Calculation of the derivative of an inaccurately defined function by means of feedback laws”, Proc. Steklov Inst. Math., 291 (2015), 219–231  mathnet  crossref  crossref  isi  elib
    6. R. R. Akopian, “Optimal recovery of an analytic function in a doubly connected domain from its approximately given boundary values”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 13–18  mathnet  crossref  mathscinet  isi  elib
    7. R. R. Akopian, “Optimal Recovery of Analytic Functions from Boundary Conditions Specified with Error”, Math. Notes, 99:2 (2016), 177–182  mathnet  crossref  crossref  mathscinet  isi  elib
    8. R. R. Akopyan, “Optimal recovery of a function analytic in a disk from approximately given values on a part of the boundary”, Proc. Steklov Inst. Math. (Suppl.), 300, suppl. 1 (2018), 25–37  mathnet  crossref  crossref  mathscinet  isi  elib
    9. Akopyan R.R., “Optimal Recovery of a Derivative of An Analytic Function From Values of the Function Given With An Error on a Part of the Boundary”, Anal. Math., 44:1 (2018), 3–19  crossref  isi
    10. R. R. Akopyan, “Optimalnoe vosstanovlenie analiticheskoi v poluploskosti funktsii po priblizhenno zadannym znacheniyam na chasti granichnoi pryamoi”, Tr. IMM UrO RAN, 24, no. 4, 2018, 19–33  mathnet  crossref  elib
    11. R. R. Akopyan, “An analogue of the two-constants theorem and optimal recovery of analytic functions”, Sb. Math., 210:10 (2019), 1348–1360  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. V. V. Arestov, R. R. Akopyan, “Zadacha Stechkina o nailuchshem priblizhenii neogranichennogo operatora ogranichennymi i rodstvennye ei zadachi”, Tr. IMM UrO RAN, 26, no. 4, 2020, 7–31  mathnet  crossref  elib
    13. R. R. Akopyan, “Analog teoremy Adamara i svyazannye ekstremalnye zadachi na klasse analiticheskikh funktsii”, Tr. IMM UrO RAN, 26, no. 4, 2020, 32–47  mathnet  crossref  elib
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